a. \(A\left(2:-3\right)\in\left(d\right)\Rightarrow-3=4m-2+2m+5\)
\(\Rightarrow m=\dfrac{3}{2}\)
\(3.y=\left(2m-1\right)x-2m+5\left(m\ne\dfrac{1}{2}\right)\)
\(\left(2;-3\right)\in\left(d\right)\Rightarrow-3=\left(2m-1\right).2-2m+5\Leftrightarrow m=-3\left(tm\right)\)
\(b,\left(d\right)//\left(d'\right)\Rightarrow\left\{{}\begin{matrix}2m-1=2\\-2m+5\ne1\\\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}m=1,5\left(tm\right)\\m\ne2\end{matrix}\right.\)
\(\Rightarrow\left(d\right):y=2x+2\)\(đi-qua-A\left(0;2\right),B\left(-1;0\right)\Rightarrow\cos\left(\alpha\right)=\dfrac{\left|OB\right|}{\left|OA\right|}=\dfrac{\left|-1\right|}{2}\Rightarrow\alpha=60^o\)
\(c,gọi-điểm-cố-định-làC\left(xo;yo\right)\Rightarrow\left(2m-1\right)xo-2m+5=yo\)
\(\Leftrightarrow2mxo-xo-2m+5-yo=0\)
\(\Leftrightarrow2m\left(xo-1\right)-xo-yo+5=0\Rightarrow\left\{{}\begin{matrix}xo=1\\yo=4\end{matrix}\right.\)
\(\Rightarrow C\left(1;4\right)là-điểm-cố-định\)
\(\)
